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Some of TWKA’s clients are: Peoples Gas Light and Coke Company, Bender Management Consultants, Salomon Smith Barney, Amoco, Natural Gas Pipeline Company of America, Newmont Gold Company, National Science Foundation, Institute of Gas Technology, Sun Oil Company, Motorola, Northern Illinois Gas Company, Office of Naval Research, North Shore Gas Company, Metropolitan Sanitary District of Cook County, Boston Energy Associates, Turner Broadcasting, Lucent Technologies, a Baby Bell, Minera Yanacocha, Eka Chemicals, Andean Flowers, Eaglebrook, Inc., the Gas Research Institute, and Continental Airlines.

The application areas covered are extremely broad, including both manufacturing and service firms. The common thread is the effective utilization of resources to satisfy constraints. Supply-chain planning and planning the extraction of ore from gold mines have this characteristic. So do optimizing bond portfolios and planning the purchase and use of natural gas. Applications are only limited by one’s imagination.

We would like to help you with your decision problem. Some representative projects are described here.

Peoples Gas Light & Coke Company  (Chicago) has been a client of  TWKA  since 1984 and continues to be one today. During this period, deregulation has caused great changes for Local Distribution Companies operating in the natural gas industry. The first planning model was a linear programming model using the LINDO optimization system on an IBM mainframe. A new generation of planning models using multiple-scenarios (with associated probabilities) resulted in large, complex models with long solution times. The system was subsequently modified for an IBM RS/6000 using IBM's Optimization Subroutine Library (OSL). The system was used as the basis for PGLC’s filing of its Integrated Resource Plan with the Illinois Commerce Commission and to analyze new supply and storage contracts. This system was used to restructure Peoples Gas supply portfolio resulting in annual savings of $44 million.

Tactical models have also been designed and implemented. A multi-year model that plans at the daily level has been developed for the creation of a 5-year profit plan. This daily model uses the LINDO system on PC computers. Another system optimizes decisions about purchases and storage activities for the next day. This system uses the What'sBest! spreadsheet optimizer.

A model for a telecommunications firm chooses the capital projects to fund so that the resulting in the portfolio of capital investments that maximized the Net Present Value. Among the considerations were each project's Net Present Value and expenditure levels, budget limitations, logical restrictions among the projects (e.g., only one of these two projects can be undertaken), business unit allocation limits, and customer service goals.

TWKA developed an integrated logistics-planning system for a firm located in Washington, DC. The decision problem has three levels, (1) multiple manufacturing plants, (2) intermediate warehousing, and (3) customer and local distribution points. The decisions are: (1) what plants should be kept open and how much should be made of each product at each plant, (2) which warehouses should be kept open and how much should be shipped of each product from each plant to each warehouse, and (3) how much of each product should be shipped from each warehouse to satisfy the demands of the customers and distribution points. The model is an integer linear programming model with fixed charge costs associated with keeping the plants and warehouses open as well as piece-wise linear operating costs caused by operating economies of scale. LINDO is used to optimize the logistics planning model based on data created by a front-end. The front-end does data input and management and management reports are created from the optimized results. The front-end data input and report generation used a database.

The deregulation of the natural gas industry lead to a project for Natural Gas Pipeline Company of America (Houston). When a company has excess capacity on a pipeline, they post the information on an electronic bulletin board. Then, other companies post their bids on the electronic bulletin board for the excess capacity. Each bid specifies the minimum and maximum volume they are willing to purchase, a bid value, and the dates that the capacity is desired. The data from the electronic bulletin board is the input for an integer linear programming model that allocates the excess capacity to the bidders so the value is maximized. The optimal solution then is uploaded to the electronic bulletin board. Complex tie-breaking procedures required the use of the LINDO system, rather than What'sBest! to solve the problem.

The number of ticket counter and gate personnel required by an airline at an airport varies depending on the timing of arrivals and departures of its flights. A web-based system was developed for  Continental Airlines that optimizes the scheduling of personnel by determining the work patterns (durations and start –times) while achieving desired service levels. The user fills out an electronic form specifying the airport’s needs and policy decisions; the form becomes the basis for an Excel worksheet that contains the data; a What'sBest! model reads the data and solves for the optimal personnel schedule. Finally, the user receives an e-mail that contains the schedule in a familiar format. Visual Basic for Applications programming provided the links; generating and solving the What'sBest! model, and exporting the optimal solution.

Research sponsored by the Office of Naval Research developed new methodologies for optimizing integrated-process quality levels and sampling plans for manufacturing systems. Extensions included the impact of possible inspector errors. One result was a large-scale computer system for optimizing manufacturing system design, with an emphasis on product quality. This system used dynamic programming for both serial and assembly manufacturing processes.

One project for Sun Oil Company was design of inventory control policies for bulk plants served by barge. Both the time between the ordering of the barge and its arrival at the bulk plant as well as demand during that period are uncertain. A model for forecasting the demand rate during the replenishment was developed. A computer simulation model was used to choose the reorder point and the order quantity. Note that the storage tanks at the bulk plant can't be overfilled.

A large telecommunications company faced expanding, but seasonal needs for employees. Options included overtime, new permanent hires, and new temporary hires.  The extensive training program and diminished service rates during a multi-month learning period after completion of the training program made new hires, either permanent or temporary, an expensive alternative.  However, hiring enough new permanent staff to achieve the desired level of service in peak months caused an excess of staff during months with small requirements. A What'sBest! model optimized the workforce to achieve the desired service levels at minimum cost.

As interest rates decrease, it may be cost effective for an agency that issues bonds to call some and refinance them. An investment banking firm uses a What'sBest! model to choose the bonds to refinance from among the outstanding bonds and the amounts and maturities of the new bonds.

A mining company needed to decide which deposits to mine, when to mine them, and which processing plant should process which deposits. An optimization model solves this decision problem.

A chemical manufacturer had variable manufacturing costs that changed based upon the production volume at each of its manufacturing plants. A What'sBest! model was developed to determine the amount to produce at each plant and how much should be sent to each customer so that the total of manufacturing and shipping costs are minimized.

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